Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sqrt{2 \sin{\left(x \right)}} - 1 = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \frac{\pi}{6}$$
$$x_{2} = \frac{5 \pi}{6}$$
Numerical solution$$x_{1} = -97.9129710368819$$
$$x_{2} = 90.5825881785057$$
$$x_{3} = 27.7507351067098$$
$$x_{4} = 75.9218224617533$$
$$x_{5} = -62.3082542961976$$
$$x_{6} = 34.0339204138894$$
$$x_{7} = 78.0162175641465$$
$$x_{8} = -236.143047794833$$
$$x_{9} = -3.66519142918809$$
$$x_{10} = -41.3643032722656$$
$$x_{11} = 94.7713783832921$$
$$x_{12} = -74.8746249105567$$
$$x_{13} = 65.4498469497874$$
$$x_{14} = -18.3259571459405$$
$$x_{15} = -53.9306738866248$$
$$x_{16} = -5.75958653158129$$
$$x_{17} = -56.025068989018$$
$$x_{18} = 25.6563400043166$$
$$x_{19} = 19.3731546971371$$
$$x_{20} = -30.8923277602996$$
$$x_{21} = -9.94837673636768$$
$$x_{22} = -91.6297857297023$$
$$x_{23} = 163.886416762268$$
$$x_{24} = 63.3554518473942$$
$$x_{25} = 2.61799387799149$$
$$x_{26} = 57.0722665402146$$
$$x_{27} = -79.0634151153431$$
$$x_{28} = -22.5147473507269$$
$$x_{29} = -60.2138591938044$$
$$x_{30} = -47.6474885794452$$
$$x_{31} = 46.6002910282486$$
$$x_{32} = -49.7418836818384$$
$$x_{33} = 82.2050077689329$$
$$x_{34} = -66.497044500984$$
$$x_{35} = 15.1843644923507$$
$$x_{36} = 8.90117918517108$$
$$x_{37} = 84.2994028713261$$
$$x_{38} = -100.007366139275$$
$$x_{39} = -81.1578102177363$$
$$x_{40} = -93.7241808320955$$
$$x_{41} = -28.7979326579064$$
$$x_{42} = 69.6386371545737$$
$$x_{43} = 6.80678408277789$$
$$x_{44} = 52.8834763354282$$
$$x_{45} = 21.4675497995303$$
$$x_{46} = -68.5914396033772$$
$$x_{47} = 13.0899693899575$$
$$x_{48} = -72.7802298081635$$
$$x_{49} = -24.60914245312$$
$$x_{50} = -16.2315620435473$$
$$x_{51} = 31.9395253114962$$
$$x_{52} = -85.3466004225227$$
$$x_{53} = -37.1755130674792$$
$$x_{54} = -12.0427718387609$$
$$x_{55} = -43.4586983746588$$
$$x_{56} = 96.8657734856853$$
$$x_{57} = 38.2227106186758$$
$$x_{58} = 0.523598775598299$$
$$x_{59} = 59.1666616426078$$
$$x_{60} = 44.5058959258554$$
$$x_{61} = -87.4409955249159$$
$$x_{62} = 88.4881930761125$$
$$x_{63} = 101.054563690472$$
$$x_{64} = 50.789081233035$$
$$x_{65} = 71.733032256967$$
$$x_{66} = -129.32889757278$$
$$x_{67} = 40.317105721069$$
$$x_{68} = -35.081117965086$$